1. solve the inequality x^2 + 5x > 14

x^2 + 5x  > 14

To
solve the inequality, first we will have to move 14 to the left side of the
inequality:

==> x^2+ 5x - 14 >
0

Now we can factor the left
side:

==> (x+ 7) (x-2 )
>0

Now we notcie that we have a product of two
functions.

In order for the product we be greater that 0,
we have two possible cases:

1. Both terms should be
positivs:

==> x+ 7 > 0     and    x-2
> 0

==> x > -7    and    x >
2

==> x belongs to the interva ( 2,
inf)

2. Both terms should be
negative:

==> x+ 7 < 0     and    x-2
< 0

==> x < -7    and   x <
2

==> x belongs to the interval ( -inf,
-7)

Then x = ( -inf, -7) U ( 2,
inf)

OR x = R -
[-7,2]